Scala analysis: xen15-gilson-aristoxenus-chromatic-malakon
Aristoxenus' Chromatic Malakon
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 2: 15/14 119.442808 major diatonic semitone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 45/29 760.646521 6: 45/28 821.397809 septimale wide minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/45 378.6022 septimal narrow major third 1: 30/29 58.6915 2: 29/28 60.7513 3: 56/45 378.6022 septimal narrow major third 4: 9/8 203.9100 major whole tone 5: 30/29 58.6915 6: 29/28 60.7513 7: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 30/29 58.692 cents 1: 2 29/28 60.751 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 56/45 378.602 cents septimal narrow major third 2: 2 15/14 119.443 cents major diatonic semitone 2: 1 135/116 262.602 cents 2: 1 112/87 437.294 cents 2: 2 58/45 439.353 cents 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 135/112 323.353 cents septimal wide minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 42/29 641.204 cents 3: 1 29/20 643.263 cents 4: 1 40/29 556.737 cents 4: 1 29/21 558.796 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 224/135 876.647 cents narrow septimal major sixth 5: 1 10/7 617.488 cents Euler's tritone 5: 2 45/29 760.647 cents 5: 1 87/56 762.706 cents 5: 1 232/135 937.398 cents 5: 2 28/15 1080.557 cents grave major seventh 6: 2 45/28 821.398 cents septimale wide minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 56/29 1139.249 cents 6: 2 29/15 1141.308 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 58.7 119.4 498.0 702.0 760.6 821.4 1200.0 58.7 : 60.8 439.4 643.3 702.0 762.7 1141.3 1200.0 119.4 : 378.6 582.5 641.2 702.0 1080.6 1139.2 1200.0 498.0 : 203.9 262.6 323.4 702.0 760.6 821.4 1200.0 702.0 : 58.7 119.4 498.0 556.7 617.5 996.1 1200.0 760.6 : 60.8 439.4 498.0 558.8 937.4 1141.3 1200.0 821.4 : 378.6 437.3 498.0 876.6 1080.6 1139.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 378.6022 cents 812/675, 319.9107 cents 30/29, 58.6915 cents 2: 119.4428 .. 582.5122 cents 98/75, 463.0694 cents 675/784,-259.1594 cents 3: 323.3528 .. 643.2635 cents 812/675, 319.9107 cents 675/784,-259.1594 cents 4: 556.7365 .. 876.6472 cents 812/675, 319.9107 cents 800/841,-86.5270 cents 5: 617.4878 .. 1080.5572 cents 98/75, 463.0694 cents 675/784,-259.1594 cents 6: 821.3978 .. 1141.3085 cents 812/675, 319.9107 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 2.920841 Largest / Average step : 2.208513 Largest / Smallest step : 6.450714 Median interval of one step : 29/28, 60.7513 cents, amount: 2 Least squares average step : 155.22251 cents, oct.: 1086.55758 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ABDCABD Scale is a Constant Structure, by a margin of 23.71591 cents Scale diversity : 1.543329 Lumma stability : 0.097819 Lumma impropriety factor : 0.800929 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 841/840, 2.0598 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 29 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.012084 Average absolute harmonicity : 0.229795 Specific harmonicity : 0.063408 Fundamental : 1/2436, -11.2503 octaves, 0.1074 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 4.384800E+05, 18.74215 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 125.0, average 17.85714 Mersenne's string divisions : 970496310 Sum of van Prooijen's expressibility: 6.89916, average 0.98559 Sum of Tenney's harmonic distance : 13.63608, average 1.94801 Vogel's harmonic complexity : 36.14286 Wille's k value : 1957 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 69.05750, average 2.46634 Lattice compactness (without 2's) : 48.84345, average 1.74441 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -1 .. 2 0.85714 8 2 5: 0 .. 1 0.57143 4 7: -1 .. 0 -0.28571 2 2 29: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 15 19 34| Scale is weakly epimorphic with val: <7 10 15 20 33| Scale is weakly epimorphic with val: <7 10 16 20 35| Scale is weakly epimorphic with val: <7 10 16 21 34| Scale is weakly epimorphic with val: <7 10 17 21 36| Scale is weakly epimorphic with val: <7 10 17 22 35| Scale is weakly epimorphic with val: <7 10 18 22 37| Scale is weakly epimorphic with val: <7 11 15 18 31| Scale is JI-epimorphic with val: <7 11 16 18 33| Scale is weakly epimorphic with val: <7 11 16 19 32| Scale is JI-epimorphic with val: <7 11 17 19 34| Scale is weakly epimorphic with val: <7 11 17 20 33| Scale is JI-epimorphic with val: <7 11 18 20 35| Scale is weakly epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 12 15 21 31| Scale is weakly epimorphic with val: <7 12 16 18 36| Scale is weakly epimorphic with val: <7 12 16 22 32| Scale is weakly epimorphic with val: <7 12 17 19 37| Scale is weakly epimorphic with val: <7 12 18 20 31|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 44.0248 c. M: 74.9322 c. 8: 0 1 2 2 0 0 3 N SD: 45.0493 c. M: 71.3978 c. 9: 0 1 3 1 1 0 3 N SD: 34.0897 c. M: 58.6915 c. 10: 0 1 3 2 0 1 3 N SD: 29.5065 c. M: 58.6915 c. 12: 1 0 4 2 1 0 4 N SD: 24.1975 c. M:-41.3085 c. 13: 1 0 4 3 0 1 4 N SD: 27.0233 c. M:-36.5065 c. 14: 1 0 5 2 1 1 4 N SD: 23.2665 c. M:-35.7450 c. 16: 1 1 5 2 1 1 5 N SD: 19.9255 c. M:-30.5572 c. 17: 1 1 5 3 1 1 5 N SD: 14.8978 c. M:-25.6610 c. 19: 1 1 6 3 1 1 6 N SD: 5.0580 c. M:-7.2182 c. 39: 2 2 12 7 2 2 12 N SD: 5.9601 c. M:-9.3714 c. 41: 2 2 13 7 2 2 13 N SD: 1.1815 c. M: 2.3696 c. 60: 3 3 19 10 3 3 19 N SD: 1.3114 c. M:-1.9550 c. 101: 5 5 32 17 5 5 32 N SD: 0.8767 c. M: 1.5958 c. 142: 7 7 45 24 7 7 45 N SD: 0.8387 c. M: 1.6795 c. 161: 8 8 51 27 8 8 51 N SD: 0.9960 c. M: 1.5220 c. 181: 9 9 57 31 9 9 57 N SD: 0.9216 c. M:-1.7844 c. 183: 9 9 58 31 9 9 58 N SD: 0.8678 c. M: 1.7257 c. 200: 10 10 63 34 10 10 63 N SD: 0.7765 c. M:-1.3535 c. 229: 11 12 72 39 11 12 72 N SD: 0.8250 c. M:-1.3096 c. 241: 12 12 76 41 12 12 76 N SD: 0.6068 c. M:-1.1792 c. 270: 13 14 85 46 13 14 85 N SD: 0.5838 c. M: 0.9137 c. 282: 14 14 89 48 14 14 89 N SD: 0.5418 c. M:-1.0556 c. 301: 15 15 95 51 15 15 95 N SD: 0.5492 c. M:-1.1091 c. 311: 15 16 98 53 15 16 98 N SD: 0.4396 c. M: 0.8137 c. 330: 16 17 104 56 16 17 104 N SD: 0.4145 c. M: 0.6465 c. 352: 17 18 111 60 17 18 111 N SD: 0.3729 c. M: 0.7370 c. 371: 18 19 117 63 18 19 117 N SD: 0.2935 c. M: 0.5387 c. 412: 20 21 130 70 20 21 130 N SD: 0.2390 c. M: 0.4523 c. 453: 22 23 143 77 22 23 143 N SD: 0.2442 c. M: 0.4134 c. 513: 25 26 162 87 25 26 162 N SD: 0.2495 c. M: 0.4126 c. 552: 27 28 174 94 27 28 174 N SD: 0.1990 c. M:-0.3413 c. 571: 28 29 180 97 28 29 180 N SD: 0.1935 c. M:-0.3470 c. 593: 29 30 187 101 29 30 187 N SD: 0.1704 c. M: 0.2372 c. 612: 30 31 193 104 30 31 193 N SD: 0.1152 c. M:-0.1708 c. 653: 32 33 206 111 32 33 206 N SD: 0.0754 c. M:-0.1498 c. 1024: 50 52 323 174 50 52 323 N SD: 0.0705 c. M: 0.0996 c. 1065: 52 54 336 181 52 54 336 N SD: 0.0502 c. M: 0.1000 c. 1658: 81 84 523 282 81 84 523 N SD: 0.0649 c. M: 0.0957 c. 1677: 82 85 529 285 82 85 529 N SD: 0.0349 c. M:-0.0691 c. 1718: 84 87 542 292 84 87 542 N SD: 0.0171 c. M: 0.0240 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5:6 S SD: 20.9870 cents 4 x x 5:6 x x 8 S SD: 37.2438 cents 5 x x 7 x x 8:10 SD: 28.2728 cents 6 x 7:8:9 x 10:12 S SD: 32.0619 cents 7 x 8:9 x 11 x 14 SD: 32.5242 cents 8 x 9:11:12 x 13:16 SD: 20.3358 cents 9 x 10:12 x 14 x 18 SD: 15.7764 cents 10 x 11:13:15 x 16:20 SD: 12.7381 cents 11 x 12:15 x 17:18:22 SD: 11.8473 cents 12 x 13:16:18 x 19:24 SD: 6.4301 cents 13 x 14:17 x 20:21:26 SD: 7.7661 cents 14 x 15:19:21:22:23:28 SD: 8.9194 cents 15 x 16:20 x 23:24:30 SD: 4.6690 cents 16 x 17:21:24:25:26:32 SD: 6.3742 cents 17 x 18:23 x 26:27:34 SD: 9.1805 cents 18 x 19:24:27:28:29:36 SD: 4.4226 cents 19:20 x 25 x 29:31:38 SD: 10.8293 cents 20:21 x 27:30:31:32:40 SD: 5.7496 cents 24:25:26:32:36:37:39:48 SD: 4.5225 cents 26:27:28:35:39:40:42:52 SD: 3.7696 cents 28:29:30:37:42:43:45:56 SD: 3.4038 cents 30:31:32:40:45:47:48:60 SD: 2.8497 cents 51:53:55:68:77:79:82:102 SD: 2.5815 cents 52:54:56:69:78:81:84:104 SD: 2.5346 cents 53:55:57:71:80:82:85:106 SD: 2.4551 cents 54:56:58:72:81:84:87:108 SD: 1.2198 cents 56:58:60:75:84:87:90:112 SD: 1.1776 cents 82:85:88:109:123:127:132:164 SD: 1.1687 cents 84:87:90:112:126:130:135:168 SD: 0.7182 cents 112:116:120:149:168:174:180:224 SD: 0.6918 cents 114:118:122:152:171:177:183:228 SD: 0.4576 cents 168:174:180:224:252:261:270:336 SD: 0.4161 cents 198:205:212:264:297:307:318:396 SD: 0.3696 cents 234:242:251:312:351:363:376:468 SD: 0.3025 cents 252:261:270:336:378:391:405:504 SD: 0.2951 cents 292:302:313:389:438:453:469:584 SD: 0.2944 cents 321:332:344:428:482:498:516:642 SD: 0.2765 cents 324:335:347:432:486:503:521:648 SD: 0.2430 cents 348:360:373:464:522:540:559:696 SD: 0.1579 cents 408:422:437:544:612:633:656:816 SD: 0.1463 cents 522:540:559:696:783:810:839:1044 SD: 0.1281 cents 576:596:617:768:864:894:926:1152 SD: 0.1251 cents